We note that the right hand side (RHS) of (REF ) provides a upper bound of the ergodic capacity. In fact, under the high SNR and low SNR, the ergodic achievable rate has the approximate expression of \(\mathbb {E}\left\lbrace  R \right\rbrace  = {\log _2}\left( {\mathbb {E}\left\lbrace  {\text{SNR}} \right\rbrace } \right)\)  and \(\mathbb {E}\left\lbrace  R \right\rbrace  = {{\mathbb {E}\left\lbrace  {\text{SNR}} \right\rbrace } \mathord {\left\bad.{\vphantom{{\mathbb {E}\left\lbrace  {\text{SNR}} \right\rbrace } {\ln 2}}} \right.\hspace{0.0pt}} {\ln 2}}\) , respectively, both of which are heavily dependent on the average SNR [1]}.
